The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14.
Given that the volume \( V = 261.8 , \text{cm}^3 \) and the height \( h = 10 , \text{cm} \), we can plug these values into the formula and solve for \( r \):
\[ 261.8 = \frac{1}{3} \pi r^2 (10) \]
Multiplying both sides by 3 to eliminate the fraction:
\[ 785.4 = \pi r^2 (10) \]
Now we divide both sides by 10:
\[ 78.54 = \pi r^2 \]
Next, we divide both sides by \( \pi \):
\[ r^2 = \frac{78.54}{\pi} \]
To approximate \( \pi \), we can use 3.14:
\[ r^2 \approx \frac{78.54}{3.14} \approx 25 \]
Now we take the square root of both sides to find \( r \):
\[ r \approx \sqrt{25} \approx 5 \]
So, the approximate radius of the cone is \( 5 , \text{cm} \).
The closest answer from the options provided is:
5